Such blow moulding machines are known in various embodiments, the preforms and the finished hollow bodies, such as bottles, being transported directly (GB 2 074496 A) or indirectly (DE 27 42 693 C2) with the aid of loose mandrels. In any case, the heating wheel and the blow wheel rotate side by side in a common horizontal plane; if necessary, an intermediate transfer device is used for the heated preforms. This inevitably results in a structural design occupying a large floor space and taking up much room. The integration of a known blow moulding machine in a filling plant for bottles or the like, which is more and more realized in practice in order to achieve a reduction of costs, or even the subsequent incorporation into an existing filling plant is therefore much more difficult.